Laminar and Turbulent Incompressible Boundary Layers on Slender Bodies of Revolution in Axial Flow

1970 ◽  
Vol 92 (3) ◽  
pp. 545-550 ◽  
Author(s):  
T. Cebeci
Keyword(s):  
Skin Friction ◽  
Boundary Layers ◽  
Incompressible Flows ◽  
Reynolds Shear Stress ◽  
Axial Flow ◽  
Velocity Profiles ◽  
Bodies Of Revolution ◽  
Local Skin ◽  
Law Of The Wall ◽  
Slender Bodies

The boundary-layer equations for both laminar and turbulent incompressible flows over slender bodies of revolution in axial flow are solved by an implicit finite-difference method. The Reynolds shear-stress term is eliminated by means of an eddy-viscosity concept. Velocity profiles and values of local skin-friction coefficient are obtained for various slender circular cylinders in both laminar and turbulent flows. The deviation of the cylinder skin friction from that of a flat plate is studied. The calculated velocity profiles for turbulent flow are compared with those of both Richmond’s and Yasuhara’s experimental data and with Rao’s proposed formulation of the law of the wall in thick, axisymmetric turbulent boundary layers. In both cases excellent agreement is obtained.

Experimental Study of Casing Boundary Layers in a Multistage Axial Compressor

1991 ◽  
Vol 113 (2) ◽  
pp. 240-244
Author(s):  
S. Venkateswaran
Keyword(s):  
Shear Stress ◽  
Skin Friction ◽  
Boundary Layers ◽  
Axial Compressor ◽  
Axial Flow ◽  
Two Dimensional ◽  
Law Of The Wall ◽  
The Law ◽  
Flow Compressor ◽  
Two Dimensional Flows

Measurements of the casing boundary layers were obtained in a four-stage, low speed axial flow compressor, to verify the ‘law of the wall’ applicability to these complex flows. Some of the available shear stress models of the two-dimensional flows have been examined towards the quantitative assessment of skin friction. The shear stress prediction obtained from the Ludwieg-Tillmann relation applied to the streamwise or untwisted profile agreed closely with the measured shear stress by the hot wire. The skin friction was fairly constant for rotor and stator flows and was close to the flat plate values. The boundary layer profiles exhibited a well pronounced semi-logarithmic region with the universal constants of the law of the wall far removed from the standard two dimensional values, especially for rotor flows. Stator flows showed signs of similarity to two dimensional flows.

Scaling of Favorable Pressure Gradient Turbulent Boundary Layers With Eventual Relaminarization

2005 ◽  
Author(s):  
Rau´l Bayoa´n Cal ◽  
Xia Wang ◽  
Luciano Castillo
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Boundary Layers ◽  
Reynolds Shear Stress ◽  
Velocity Profiles ◽  
Turbulent Boundary Layers ◽  
Reynolds Stresses ◽  
Mean Velocity ◽  
Favorable Pressure Gradient ◽  
The Mean

Applying similarity analysis to the RANS equations of motion for a pressure gradient turbulent boundary layer, Castillo and George [1] obtained the scalings for the mean deficit velocity and the Reynolds stresses. Following this analysis, Castillo and George studied favorable pressure gradient (FPG) turbulent boundary layers. They were able to obtain a single curve for FPG flows when scaling the mean deficit velocity profiles. In this study, FPG turbulent boundary layers are analyzed as well as relaminarized boundary layers subjected to an even stronger FPG. It is found that the mean deficit velocity profiles diminish when scaled using the Castillo and George [1] scaling, U∞, and the Zagarola and Smits [2] scaling, U∞δ*/δ. In addition, Reynolds stress data has been analyzed and it is found that the relaminarized boundary layer data decreases drastically in all components of the Reynolds stresses. Furthermore, it will be shown that the shape of the profile for the wall-normal and Reynolds shear stress components change drastically given the relaminarized state. Therefore, the mean velocity deficit profiles as well as Reynolds stresses are found to be necessary in order to understand not only FPG flows, but also relaminarized boundary layers.

The Computation of Thick Axisymmetric Boundary Layers and Wakes around Bodies of Revolution

1984 ◽  
Vol 198 (1) ◽  
pp. 51-62 ◽  
Author(s):  
N C Markatos
Keyword(s):  
Boundary Layers ◽  
Pressure Coefficient ◽  
Three Dimensional ◽  
Normal Pressure ◽  
Velocity Profiles ◽  
The Body ◽  
Tail Region ◽  
Full Account ◽  
Bodies Of Revolution ◽  
Experimental Values

The paper is concerned with the computational investigation of thick, axisymmetric, turbulent boundary layers and wakes around bodies of revolution. The procedures employed take full account of the influence of longitudinal and transverse surface curvatures and normal pressure gradients on the development of the boundary layer and wake, and also the viscous—inviscid interaction in the tail region of the body. The method makes it possible to calculate the static pressure and the velocity profiles along the body as well as the drag components; and it is applicable to both two- and three-dimensional situations, enabling, for example, the prediction of flows around ships' and submarines' hulls to be made. The application of the fully-elliptic calculation procedure to a body of revolution is described, and comparisons made between predictions and experimental measurements. The calculated axial variation of skin friction and pressure coefficient, and the velocity profiles are shown to be in fair agreement with experimental values.

scholarly journals Evolution and structure of sink-flow turbulent boundary layers

2001 ◽  
Vol 428 ◽  
pp. 1-27 ◽  
Author(s):  
M. B. JONES ◽  
IVAN MARUSIC ◽  
A. E. PERRY
Keyword(s):  
Boundary Layers ◽  
Velocity Profiles ◽  
Turbulent Boundary Layers ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Mean Velocity ◽  
Flow Measurements ◽  
Law Of The Wall ◽  
The Mean ◽  
Logarithmic Law

An experimental and theoretical investigation of turbulent boundary layers developing in a sink-flow pressure gradient was undertaken. Three flow cases were studied, corresponding to different acceleration strengths. Mean-flow measurements were taken for all three cases, while Reynolds stresses and spectra measurements were made for two of the flow cases. In this study attention was focused on the evolution of the layers to an equilibrium turbulent state. All the layers were found to attain a state very close to precise equilibrium. This gave equilibrium sink flow data at higher Reynolds numbers than in previous experiments. The mean velocity profiles were found to collapse onto the conventional logarithmic law of the wall. However, for profiles measured with the Pitot tube, a slight ‘kick-up’ from the logarithmic law was observed near the buffer region, whereas the mean velocity profiles measured with a normal hot wire did not exhibit this deviation from the logarithmic law. As the layers approached equilibrium, the mean velocity profiles were found to approach the pure wall profile and for the highest level of acceleration Π was very close to zero, where Π is the Coles wake factor. This supports the proposition of Coles (1957), that the equilibrium sink flow corresponds to pure wall flow. Particular interest was also given to the evolutionary stages of the boundary layers, in order to test and further develop the closure hypothesis of Perry, Marusic & Li (1994). Improved quantitative agreement with the experimental results was found after slight modification of their original closure equation.

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